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A Beautiful Mind
1．John Forbes Nash, Jr. –mathematical genius, inventor of a theory of rationed behavior, visionary of the thinking machine—had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll’s, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. “How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof… how could you believe that extraterrestrials are sending you message? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”
小约翰· 福布斯· 纳什，数学天才、理性行为理论创立者、预见会思考的机器出现的预言者，已经和他的同样是数学家的来访者一起坐了差不多半个小时.那是1959年春季一个工作日的傍晚时分，虽然才是5 月，天气却很热，令人不太舒服。纳什颓然坐在医院会客室一角的扶手椅上，身上随意穿着的那件尼龙衬衫，松松垮垮地盖在他没有系皮带的长裤上。他的魁梧身躯现在就像一个布娃娃一样缺乏活力，他的线条优美细致的五官没有任何表情。他一直目
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光呆滞地盯着哈佛教授乔治· 麦基左脚前方不远的地方，除了一次次重复着将垂在前额的略长的黑发拨开的动作，他几乎一动不动。麦基正襟危坐，被沉默压得透不过气来，并且非常清楚地意识到会客室的所有门都锁上了。麦基再也控制不住自己。他尽量使语气温和，但听上去仍有些愠怒。“你，一个数学家，”他开始说道，“一个致力于研究理性和逻辑证明的人，怎么能相信外星人正在给你发送消息呢？怎么能相信你被来自太空的外星人选中要来拯救世界呢？怎么能??”
2．Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”
纳什终于抬起头，用类似某种鸟类或者蛇一样冰冷而不动声色的目光，紧紧盯着麦基。“因为，”他慢慢地回答，带着温和适度的南方人特有的慢条斯理的语气，好像自言自语一般，“我的有关超自然生物的想法出现在我的脑海里的方式，是和我的数学思想一样的，所以我会认真对待。”
3．The young genius from Bluefield, West Virginia—handsome, arrogant, and highly eccentric—burst onto the mathematical scene in 1948. Over the next decade, a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind’s survival, Nash proved himself, in the words of the eminent geometer Mikhail Gromov, “the most remarkable mathematician of the second half of the century”. Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary spaces, the mystery of prime numbers—all
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engaged his wide-ranging imagination. His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions.
这个来自西弗吉尼亚州布卢菲尔德的年轻天才——英俊、傲慢，而且非常古怪——在1948 年闯入数学界。在接下来的十年，在那既以对人类理性抱有无上信念而著称，又以对人类生存怀有无尽忧虑而闻名的十年，纳什，用知名几何学家米克哈尔· 格罗莫夫的话说，证明了自己是“20 世纪后半叶最杰出的数学家”。策略博弈、经济竞争、计算机建筑学、宇宙的形状、虚构空间的几何学、素数的神秘，都是他广阔的想象力涉猎的领域。他的想法属于那种非常深奥而又完全出人意料的类型，无疑会推动科学思考进入新的方向。
4．Geniuses, the mathematician Paul Halmos wrote, “are of two kinds: the ones who are just like all of us, but very much more so, and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue”. Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences: It wasn’t merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were nonrational. Like other great mathematical intuitionist — Georg Friedrich Bernhard Riemann, Jules Henri Poincare, Srinivasa Rammanujan — Nash saw the vision first; constructing the laborious proofs long afterward. But even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about him that “everyone else would climb a peak by looking for a path somewhere on the mountain. Nash would climb another mountain altogether and from that
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distant peak would shine a searchlight back onto the first peak”.
数学家保罗· 哈莫斯写道，天才“分为两种：一种就像我们大家一样，只是更为出色；另一种则是那些明显具备超凡人类灵感的人。我们都能跑步，有些人还能在四分钟内跑完一英里；但是我们大多数人所做的一切无论如何也无法与谱写出Ｇ小调赋格曲相提并论”。纳什的天分就属于那种常与音乐和艺术而非与最古老的科学紧密相连的神奇异禀。这不仅仅是指他的头脑运转更加灵敏，记忆力更加出众，或是他更能集中精力。事实上，直觉的火花稍纵即逝，不能用常理解释。就像其他伟大的数学直觉大师格奥尔格· 费里德里希· 伯恩哈德· 黎曼、朱尔斯· 亨利· 庞加莱、斯里尼瓦萨· 拉马努金一样，纳什先看到一个结论，然后才开始构筑耗费心力的证明过程。不过，即便在他尝试解释某个令人震惊的结论之后，对于那些企图跟随他的逻辑的人而言，他所选择的真正途径却始终是一个谜。20 世纪50 年代就在麻省理工学院认识纳什的唐纳德· 纽曼曾经这样描述他“其他人通常会在山上寻找攀登顶峰的道路。纳什却干脆爬上另外一座山，再反过来从那个遥远的山峰用探照灯照射这座山。”
5．No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence. As a young man he was surrounded by the high priests of twentieth-century science—Albert Einstein, John von Neumann, and Norbert Wiener—but he joined no school, became no one’s disciple, got along: largely without guides or followers. In almost everything he did—from game theory to geometry—he thumbed his nose at the received wisdom, current fashions, established methods. He almost always worked alone, in his head, usually walking, often whistling Bach. Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered, but by rediscovering their truths for
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